Variable Step-Counting Times for Rietveld Analysis, or, Getting the Most Out of Your Experiment Time

Abstract

AbstractThe magnitudes of the peak intensities in a powder diffraction pattern are not uniformly distributed as a function of diffraction angle. The Lorentz-polarization factor, X-ray form-factor and the thermal vibration parameters all conspire to progressively decrease the intensities of the peaks as sinθ/λ increases. In spite of this, diffraction data for Rietveld analysis is universally collected using the same counting time for each step in the pattern. As a result, peaks at high angles are collected with lower counting precision than those at low angles, despite the fact that the high-angle region has a higher density of peaks and therefore contains more information than the low-angle part of the pattern. Indeed, the intensity, position and profile of reflections at medium and high sinθ/λ are often more easily modelled since they are subject to less interference from systematic effects such as extinction, specimen transparency and α1/α2 overlap errors. In the present work a novel variable step-counting-time regime has been devised that increases the counting times with diffraction angle in a manner inversely proportional to the intensity fall-off calculated from the Lorentz-polarization, form-factor and thermal parameters. The effect of this new data collection regime on the results of Rietveld refinement of a number of materials of varying structural complexity is discussed.